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The interference imposes a significant negative impact on the performance of wireless networks. With the continuous deployment of larger and more sophisticated wireless networks, reducing interference in such networks is quickly being…
Persistence diagrams, the most common descriptors of Topological Data Analysis, encode topological properties of data and have already proved pivotal in many different applications of data science. However, since the (metric) space of…
Subgraph isomorphism counting is known as #P-complete and requires exponential time to find the accurate solution. Utilizing representation learning has been shown as a promising direction to represent substructures and approximate the…
Graph labeling is a technique that assigns unique labels or weights to the vertices or edges of a graph, often used to analyze and solve various graph-related problems. There are few methods with certain limitations conducted by researchers…
A colored graph is a directed graph in which nodes or edges have been assigned colors that are not necessarily unique. Observability problems in such graphs consider whether an agent observing the colors of edges or nodes traversed on a…
Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs). Concurrently, topological descriptors based on persistent…
The topological Tverberg theorem has been generalized in several directions by setting extra restrictions on the Tverberg partitions. Restricted Tverberg partitions, defined by the idea that certain points cannot be in the same part, are…
A method for improving the efficiency of graph isomorphism testing is presented. The method uses the structure of the graph colored by vertex hash codes as a means of partitioning vertices into equivalence classes, which in turn reduces the…
Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…
Real data collected from different applications that have additional topological structures and connection information are amenable to be represented as a weighted graph. Considering the node labeling problem, Graph Neural Networks (GNNs)…
Despite remarkable success in diverse web-based applications, Graph Neural Networks(GNNs) inherit and further exacerbate historical discrimination and social stereotypes, which critically hinder their deployments in high-stake domains such…
Many NLP applications can be framed as a graph-to-sequence learning problem. Previous work proposing neural architectures on this setting obtained promising results compared to grammar-based approaches but still rely on linearisation…
We consider the level of information security provided by random linear network coding in network scenarios in which all nodes comply with the communication protocols yet are assumed to be potential eavesdroppers (i.e. "nice but curious").…
Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static…
The theory of colorful graphs can be developed by working in Galois field modulo (p), p > 2 and a prime number. The paper proposes a program of possible conversion of graph theory into a pleasant colorful appearance. We propose to paint the…
One method to obtain a proper vertex coloring of graphs using a reasonable number of colors is to start from any arbitrary proper coloring and then repeat some local re-coloring techniques to reduce the number of color classes. The Grundy…
The applications of graph coloring are diverse and many so lots of new types of coloring are being proposed and explored. Here we define a safe k-coloring, motivated by the application of coloring to secret sharing. Secret sharing is a way…
Graph neural networks (GNNs) have attracted much attention due to their ability to leverage the intrinsic geometries of the underlying data. Although many different types of GNN models have been developed, with many benchmarking procedures…
A mixed graph contains (undirected) edges as well as (directed) arcs, thus generalizing undirected and directed graphs. A proper coloring $c$ of a mixed graph $G$ assigns a positive integer to each vertex such that $c(u)\neq c(v)$ for every…
Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…